You are a biochemist, working with a 12-slot centrifuge. This is a gadget
that has 12 equally spaced slots around a central axis, in which you can
place chemical samples you want centrifuged. When the machine is turned on,
the samples whirl around the central axis and do their thing.

To ensure that the samples are evenly mixed, they must be distributed in the
12 slots such that the centrifuge is balanced evenly. For example, if you
wanted to mix 4 samples, you could place them in slots 12, 3, 6 and 9
(assuming the slots are numbered from 1 to 12 like a clock).